Question

The lighting department of a city has installed 2000 electric lamps with an average life of 1000 hrs and a standard deviation of 200 hrs. (10 Points) a. After what period of lighting hours would we expect 10% of the lamps to fail? b. How many lamps may be expected to fail between 900 and 1300 hrs?

Answer 1

given,

installed electric lamp = 2000

average life = 1000 hrs

standard deviation = 200 hrs

a)

let after p hors 10% bulb fails ,

P(X<p) = 0.10

`P(X< (x-\mu)/(\sigma))= 0.10`

from Normal distribution table,

P(Z<-1.28) = 0.10

on comparing

`(x-\mu)/(\sigma) = -1.28`

`(x-1000)/(200) = -1.28`

x = -1.28 x 200 + 1000

x = 744 hours

b) P( 900 < X < 1300) =

=
`P((900 -1000)/(200) < Z <(1300-1000)/(200))`

= P(-0.5 < Z < 1 .5)

= P(Z<1.5) - P(Z<-0.5)

= 0.93319 - 030854

= 0.62465

lamps may be expected to fail between 900 and 1300

= 0.62465*2000

= 1249.3

= 1249 (approx)